This paper goes beyond the optimal trading Mean Field Game model introduced by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and Lehalle, C.-A., Mean field game of controls and an application to trade crowding, Mathematics and Financial Economics (2018)]. It starts by extending it to portfolios of correlated instruments. This leads to several original contributions: first that hedging strategies naturally stem from optimal liquidation schemes on portfolios. Second we show the influence of trading flows on naive estimates of intraday volatility and correlations. Focussing on this important relation, we exhibit a closed form formula expressing standard estimates of correlations as a function of the underlying correlations and the initial imbalance of large orders, via the optimal flows of our mean field game between traders. To support our theoretical findings, we use a real dataset of 176 US stocks from January to December 2014 sampled every 5 minutes to analyze the influence of the daily flows on the observed correlations. Finally, we propose a toy model based approach to calibrate our MFG model on data.

We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price dynamics and profitability either within deterministic models or by simulation. Our novel formulation lends itself to analytic treatment even in the stochastic case. We prove conditions for the (stochastic) stability of the price process, and also for the price to mean-revert to the fundamental value. Assuming stability, we derive analytic formulae on how the population ratios influence price dynamics and the profitability of the strategies. Our results suggest that whichever trader type is more present in the market will achieve higher returns.

We present a detailed bubble analysis of the Bitcoin to US Dollar price dynamics from January 2012 to February 2018. We introduce a robust automatic peak detection method that classifies price time series into periods of uninterrupted market growth (drawups) and regimes of uninterrupted market decrease (drawdowns). In combination with the Lagrange Regularisation Method for detecting the beginning of a new market regime, we identify 3 major peaks and 10 additional smaller peaks, that have punctuated the dynamics of Bitcoin price during the analyzed time period. We explain this classification of long and short bubbles by a number of quantitative metrics and graphs to understand the main socio-economic drivers behind the ascent of Bitcoin over this period. Then, a detailed analysis of the growing risks associated with the three long bubbles using the Log-Periodic Power Law Singularity (LPPLS) model is based on the LPPLS Confidence Indicators, defined as the fraction of qualified fits of the LPPLS model over multiple time windows. Furthermore, for various fictitious `present' times t2 before the crashes, we employ a clustering method to group the predicted critical times tc of the LPPLS fits over different time scales, where tc is the most probable time for the ending of the bubble. Each cluster is proposed as a plausible scenario for the subsequent Bitcoin price evolution. We present these predictions for the three long bubbles and the four short bubbles that our time scale of analysis was able to resolve. Overall, our predictive scheme provides useful information to warn of an imminent crash risk.

Diversity is a central concept in many fields. Despite its importance, there is no unified methodological framework to measure diversity and its three components of variety, balance and disparity. Current approaches take into account disparity of the types by considering their pairwise similarities. Pairwise similarities between types do not adequately capture total disparity, since they fail to take into account in which way pairs are similar. Hence, pairwise similarities do not discriminate between similarity of types in terms of the same feature and similarity of types in terms of different features. This paper presents an alternative approach which is based similarities of features between types over the whole set. The proposed measure of diversity properly takes into account the aspects of variety, balance and disparity, and without having to set an arbitrary weight for each aspect of diversity. Based on this measure, the 'ABC decomposition' is introduced, which provides separate measures for the variety, balance and disparity, allowing them to enter analysis separately. The method is illustrated by analyzing the industrial diversity from 1850 to present while taking into account the overlap in occupations they employ. Finally, the framework is extended to take into account disparity considering multiple features, providing a helpful tool in analysis of high-dimensional data.

We propose a family of stochastic volatility models that enable predictive estimation of time-varying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has an explicit, closed-form expression for its conditional probability density function, which enables straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of the log-volatility's mean absolute innovation. These models thus can accommodate conditional power law-tail behavior ranging from very weakly non-Gaussian to Cauchy-like tails. Closed-form expressions for the models' conditional polynomial moments also allows for volatility modeling. We provide a straightforward, probabilistic method-of-moments estimation procedure that uses an asymptotic result for the process' conditional large deviation probabilities. We demonstrate the estimator's usefulness with a simulation study. We then give an empirical application, which shows that this simple modeling method can be effectively used for dynamic and predictive tail inference in heavy-tailed financial time series.

In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known law of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. A substantial part of our study is devoted to the problem of estimating fair risk allocations for expected shortfall. We study this problem under normality as well as in a nonparametric setup. We derive several estimators, and prove their fairness and/or asymptotic fairness. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. The paper closes with a substantial numerical study of the subject.

The gig economy, where employees take short-term, project-based jobs, is increasingly spreading all over the world. In this paper, we investigate the employer's and the worker's behavior in the gig economy with a dynamic principal-agent model. In our proposed model the worker's previous decisions influence his later decisions through his dynamically changing participation constraint. He accepts the contract offered by the employer when his expected utility is higher than the irrational valuation of his effort's worth. This reference point is based on wages he achieved in previous rounds. We formulate the employer's stochastic control problem and derive the solution in the deterministic limit. We obtain the feasible net wage of the worker, and the profit of the employer. Workers who can afford to go unemployed and need not take a gig at all costs will realize high net wages. Conversely, far-sighted employers who can afford to stall production will obtain high profits.

How do macro-financial shocks affect investor behavior and market dynamics? Recent evidence on experience effects suggests a long-lasting influence of personally experienced outcomes on investor beliefs and investment, but also significant differences across older and younger generations. We formalize experience-based learning in an OLG model, where different cross-cohort experiences generate persistent heterogeneity in beliefs, portfolio choices, and trade. The model allows us to characterize a novel link between investor demographics and the dependence of prices on past dividends, while also generating known features of asset prices, such as excess volatility and return predictability. The model produces new implications for the cross-section of asset holdings, trade volume, and investors' heterogenous responses to recent financial crises, which we show to be in line with the data.

Space conditioning, and cooling in particular, is a key factor in human productivity and well-being across the globe. During the 21st century, global cooling demand is expected to grow significantly due to the increase in wealth and population in sunny nations across the globe and the advance of global warming. The same locations that see high demand for cooling are also ideal for electricity generation via photovoltaics (PV). Despite the apparent synergy between cooling demand and PV generation, the potential of the cooling sector to sustain PV generation has not been assessed on a global scale. Here, we perform a global assessment of increased PV electricity adoption enabled by the residential cooling sector during the 21st century. Already today, utilizing PV production for cooling could facilitate an additional installed PV capacity of approximately 540 GW, more than the global PV capacity of today. Using established scenarios of population and income growth, as well as accounting for future global warming, we further project that the global residential cooling sector could sustain an added PV capacity between 20-200 GW each year for most of the 21st century, on par with the current global manufacturing capacity of 100 GW. Furthermore, we find that without storage, PV could directly power approximately 50% of cooling demand, and that this fraction is set to increase from 49% to 56% during the 21st century, as cooling demand grows in locations where PV and cooling have a higher synergy. With this geographic shift in demand, the potential of distributed storage also grows. We simulate that with a 1 m$^3$ water-based latent thermal storage per household, the fraction of cooling demand met with PV would increase from 55% to 70% during the century. These results show that the synergy between cooling and PV is notable and could significantly accelerate the growth of the global PV industry.

We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability if the market admits statistical arbitrage opportunities which we term $\rho$-arbitrage for a risk measure $\rho$. We show how to determine analytically whether such portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether expected shortfall constraints are ineffective in these markets. We find that the answer depends heavily upon the probability model selected by the risk manager but that it is certainly possible for expected shortfall constraints to be ineffective in realistic markets. Since value at risk constraints are weaker than expected shortfall constraints, our results can be applied to value at risk.